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Toom's Rule
Toom's rule is a 2-dimensional cellular automaton model created by Andrei Toom Andrei Leonovich Toom (in Russian: Андрей Леонович Тоом), also known as André Toom, (1942 Tashkent, Soviet Union - 2022 Queens, New York City) was a Russian mathematician known for the Toom–Cook algorithm and Toom's rule. T ... in 1978. This model is both more robust and simpler than the 2-dimensional majority vote rule. Toom's rule is a cellular automaton that acts on a 2-dimensional square lattice. At each site in this lattice is a spin with the value +1 or -1. At time t=0 the bits are initialized to some value. At each discrete time step (t>0) the lattice evolves according to Toom's rule. This rule is applied at each site simultaneously. A deterministic version of Toom's rule can be stated simply as: At each site in the lattice if the spin of the current (center) site plus the neighboring spin to the North plus the neighboring spin to the East is greater than 0, then th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cellular Automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of ''cells'', each in one of a finite number of '' states'', such as ''on'' and ''off'' (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its ''neighborhood'' is defined relative to the specified cell. An initial state (time ''t'' = 0) is selected by assigning a state for each cell. A new ''generation'' is created (advancing ''t'' by 1), according to some fixed ''rule'' (generally, a mathematical function) that determines the new state of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrei Toom
Andrei Leonovich Toom (in Russian: Андрей Леонович Тоом), also known as André Toom, (1942 Tashkent, Soviet Union - 2022 Queens, New York City) was a Russian mathematician known for the Toom–Cook algorithm and Toom's rule. Toom was a retired professor of the statistics department at Federal University of Pernambuco in Brazil. Toom died of unknown causes at his apartment in Flushing, Queens, NYC. Toom was a student of Ilya Piatetski-Shapiro Ilya Piatetski-Shapiro (Hebrew: איליה פיאטצקי-שפירו; russian: Илья́ Ио́сифович Пяте́цкий-Шапи́ро; 30 March 1929 – 21 February 2009) was a Soviet-born Israeli mathematician. During a career that sp .... ReferencesHis personal Website [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Cellular Automaton
Stochastic cellular automata or probabilistic cellular automata (PCA) or random cellular automata or locally interacting Markov chains are an important extension of cellular automaton. Cellular automata are a discrete-time dynamical system of interacting entities, whose state is discrete. The state of the collection of entities is updated at each discrete time according to some simple homogeneous rule. All entities' states are updated in parallel or synchronously. Stochastic Cellular Automata are CA whose updating rule is a stochastic one, which means the new entities' states are chosen according to some probability distributions. It is a discrete-time random dynamical system. From the spatial interaction between the entities, despite the simplicity of the updating rules, complex behaviour may emerge like self-organization. As mathematical object, it may be considered in the framework of stochastic processes as an interacting particle system in discrete-time. See for a more det ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toom Density
Toom may refer to: * Toom (surname) * Toom (Netherlands), a hamlet * Toom (supermarket), a chain of supermarkets in Germany; see Minimal (supermarket) The brand Minimal (written miniMAL in official usage) was used for a former chain of full-service supermarkets that was operated in Germany and Poland by Rewe Group until 2006. History The first Minimal store was opened in 1973 by the Bad Ho ... * Toum, a garlic sauce from Lebanon (alternative spelling) * ''Time Out of Mind'' (Bob Dylan album), 1997 {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ising Model
The Ising model () (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors. Neighboring spins that agree have a lower energy than those that disagree; the system tends to the lowest energy but heat disturbs this tendency, thus creating the possibility of different structural phases. The model allows the identification of phase transitions as a simplified model of reality. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition. The Ising model was invented by the physicist , who gave it as a prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
